Self-consistent model of the dusty torus around HL Tauri

We present the first comprehensive two-dimensional radiative transfer modeling of the circumstellar dusty environment of HL Tau, a remarkable embedded young stellar object often considered a prototype low-mass star, with a circumstellar disk that resembles the solar nebula at the early stages of planet formation. To recover its general structure and physical parameters, we used the entire beam-matched spectral energy distribution from optical to millimeter wavelengths, high-resolution intensity and linear polarization maps at 0.7, 1.25, 1.65, and 2.2 mu m (the R, J, H, and K bands), aperture synthesis maps at 1.36, 2.7, 3.06, and 7 mm, visibilities at 650 mu m, 870 mu m, and 1.36 mm, and large-aperture linear polarization measurements in the optical and near-infrared bands as observational constraints. Our detailed model of HL Tau explains all these observations well, making the overall picture much more certain. The central radiation source, with a bolometric luminosity of 11 L., is embedded in a compact, dense torus having a p oc proportional to r(-1.25) density distribution and containing predominantly very large dust particles (radii a greater than or similar to 0.1 mm). With two wide bipolar cones excavated by the out flow along the symmetry axis, the model torus has an opening angle of 90 degrees, a radius of similar to 100 AU, maximum molecular hydrogen density of 1.6 x 10(12) cm(-3), and a mass of 0.03 M. (assuming a dust-to-gas mass ratio of 0.01). A relatively large reservoir of circumstellar material, containing dust grains of submicron sizes, resides in an extended toroidal envelope of a similar mass, having a p proportional to r(-2) density profile to the adopted outer radius of 10(4) AU. The model of HL Tau strongly suggests that only the bright parts of the dense compact torus inclined toward us by similar to 43 degrees can be seen by observers at any relevant wavelength. Direct light from the central source is heavily diluted even in the highest resolution 0 ".2 images. The dusty torus is optically thick up to millimeter wavelengths, with the total optical depth of tau(V) approximate to 33 toward the invisible central object. The optical depth is partly due to the gray extinction by very large particles in the dense torus (t(V) approximate to 10) and to the wavelength-dependent extinction by submicron-sized grains in the extended envelope (tau(V) approximate to 20). If the very broad size distribution of solid particles indeed exists in the dense torus, this might indicate that in HL Tau we are observing initial phases of the accumulation of larger bodies, which may eventually lead to planet formation.